• Title/Summary/Keyword: finitely embedded

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SOME REMARKS ON COAASSOCIATED PRIMES

  • Divaani-Aazar, K.;Tousi, M.
    • Journal of the Korean Mathematical Society
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    • v.36 no.5
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    • pp.847-853
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    • 1999
  • The purpose of this paper is to develop the theory of coassociated primes and to investigate Melkersson's question [8].

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CYCLIC SUBGROUP SEPARABILITY OF HNN EXTENSIONS

  • Kim, Goansu
    • Bulletin of the Korean Mathematical Society
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    • v.30 no.2
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    • pp.285-293
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    • 1993
  • In [4], Baumslag and Tretkoff proved a residual finiteness criterion for HNN extensions (Theorem 1.2, below). This result has been used extensively in the study of the residual finiteness of HNN extensions. Note that every one-relator group can be embedded in a one-relator group whose relator has zero exponent sum on a generator, and the latter group can be considered as an HNN extension. Hence the properties of an HNN extension play an important role in the study of one-relator groups [3], [2]. In this paper we prove a criterion for HNN extensions to be .pi.$_{c}$(Theorem 2.2). Moreover, we can prove that certain one-relator groups, known to be residually finite, are actually .pi.$_{c}$. It was known by Mostowski [10] that the word problem is solvable for finitely presented, residually finite groups. In the same way, the power problem is solvable for finitely presented .pi.$_{c}$ groups. Another application of subgroup separability with respect to special subgroups was mentioned by Thurston [12, Problem 15].m 15].

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Restrictions on the Entries of the Maps in Free Resolutions and $SC_r$-condition

  • Lee, Kisuk
    • Journal of Integrative Natural Science
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    • v.4 no.4
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    • pp.278-281
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    • 2011
  • We discuss an application of 'restrictions on the entries of the maps in the minimal free resolution' and '$SC_r$-condition of modules', and give an alternative proof of the following result of Foxby: Let M be a finitely generated module of dimension over a Noetherian local ring (A,m). Suppose that $\hat{A}$ has no embedded primes. If A is not Gorenstein, then ${\mu}_i(m,A){\geq}2$ for all i ${\geq}$ dimA.

Finding Weighted Sequential Patterns over Data Streams via a Gap-based Weighting Approach (발생 간격 기반 가중치 부여 기법을 활용한 데이터 스트림에서 가중치 순차패턴 탐색)

  • Chang, Joong-Hyuk
    • Journal of Intelligence and Information Systems
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    • v.16 no.3
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    • pp.55-75
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    • 2010
  • Sequential pattern mining aims to discover interesting sequential patterns in a sequence database, and it is one of the essential data mining tasks widely used in various application fields such as Web access pattern analysis, customer purchase pattern analysis, and DNA sequence analysis. In general sequential pattern mining, only the generation order of data element in a sequence is considered, so that it can easily find simple sequential patterns, but has a limit to find more interesting sequential patterns being widely used in real world applications. One of the essential research topics to compensate the limit is a topic of weighted sequential pattern mining. In weighted sequential pattern mining, not only the generation order of data element but also its weight is considered to get more interesting sequential patterns. In recent, data has been increasingly taking the form of continuous data streams rather than finite stored data sets in various application fields, the database research community has begun focusing its attention on processing over data streams. The data stream is a massive unbounded sequence of data elements continuously generated at a rapid rate. In data stream processing, each data element should be examined at most once to analyze the data stream, and the memory usage for data stream analysis should be restricted finitely although new data elements are continuously generated in a data stream. Moreover, newly generated data elements should be processed as fast as possible to produce the up-to-date analysis result of a data stream, so that it can be instantly utilized upon request. To satisfy these requirements, data stream processing sacrifices the correctness of its analysis result by allowing some error. Considering the changes in the form of data generated in real world application fields, many researches have been actively performed to find various kinds of knowledge embedded in data streams. They mainly focus on efficient mining of frequent itemsets and sequential patterns over data streams, which have been proven to be useful in conventional data mining for a finite data set. In addition, mining algorithms have also been proposed to efficiently reflect the changes of data streams over time into their mining results. However, they have been targeting on finding naively interesting patterns such as frequent patterns and simple sequential patterns, which are found intuitively, taking no interest in mining novel interesting patterns that express the characteristics of target data streams better. Therefore, it can be a valuable research topic in the field of mining data streams to define novel interesting patterns and develop a mining method finding the novel patterns, which will be effectively used to analyze recent data streams. This paper proposes a gap-based weighting approach for a sequential pattern and amining method of weighted sequential patterns over sequence data streams via the weighting approach. A gap-based weight of a sequential pattern can be computed from the gaps of data elements in the sequential pattern without any pre-defined weight information. That is, in the approach, the gaps of data elements in each sequential pattern as well as their generation orders are used to get the weight of the sequential pattern, therefore it can help to get more interesting and useful sequential patterns. Recently most of computer application fields generate data as a form of data streams rather than a finite data set. Considering the change of data, the proposed method is mainly focus on sequence data streams.